The System of Microstresses in Cold-Worked Metal

Smith and Stickley have measured the x-ray line widths from specimens of cold-worked $\alpha$-brass and tungsten as functions of Bragg angle and x-ray wave-length. Their results accord with the microstress theory of broadening. They find that with $\alpha$-brass, which is elastically anisotropic, the line width depends upon crystallographic direction in a systematic manner, while with tungsten, which is elastically isotropic, it does not. For several very simple theoretical models of internal-stress systems the variation in line width with crystallographic direction is computed here. The one which fits the above results best, though poorly, is that which assumes that the homogeneously strained domains suffer uniform normal stress of random magnitude. A plausible model for the microstress system and a very good fit are obtained by superposing upon this model any of the other models considered and thus obtaining the proper amount of anisotropy.